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        <h1>
          <span class="m-breadcrumb"><a href="Algorithms.html">Taskflow Algorithms</a> &raquo;</span>
          Parallel Reduction
        </h1>
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          <h3>Contents</h3>
          <ul>
            <li><a href="#ParallelReductionInclude">Include the Header</a></li>
            <li><a href="#A2ParallelReduction">Create a Parallel-Reduction Task</a></li>
            <li><a href="#ParallelReductionCaptureIteratorsByReference">Capture Iterators by Reference</a></li>
            <li><a href="#A2ParallelTransformationReduction">Create a Parallel-Transform-Reduction Task</a></li>
            <li><a href="#ParallelReductionCfigureAPartitioner">Configure a Partitioner</a></li>
          </ul>
        </nav>
<p>Taskflow provides template function that constructs a task to perform parallel reduction over a range of items.</p><section id="ParallelReductionInclude"><h2><a href="#ParallelReductionInclude">Include the Header</a></h2><p>You need to include the header file, <code>taskflow/algorithm/reduce.hpp</code>, for creating a parallel-reduction task.</p><pre class="m-code"><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;taskflow/algorithm/reduce.hpp&gt;</span></pre></section><section id="A2ParallelReduction"><h2><a href="#A2ParallelReduction">Create a Parallel-Reduction Task</a></h2><p>The reduction task created by tf::Taskflow::reduce(B first, E last, T&amp; result, O bop, P&amp;&amp; part) performs parallel reduction over a range of elements specified by <code>[first, last)</code> using the binary operator <code>bop</code> and stores the reduced result in <code>result</code>. It represents the parallel execution of the following reduction loop:</p><pre class="m-code"><span class="k">for</span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">itr</span><span class="o">=</span><span class="n">first</span><span class="p">;</span><span class="w"> </span><span class="n">itr</span><span class="o">&lt;</span><span class="n">last</span><span class="p">;</span><span class="w"> </span><span class="n">itr</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w">  </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bop</span><span class="p">(</span><span class="n">result</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">itr</span><span class="p">);</span>
<span class="p">}</span></pre><p>At runtime, the reduction task spawns a subflow to perform parallel reduction. The reduced result is stored in <code>result</code> that will be captured by reference in the reduction task. It is your responsibility to ensure <code>result</code> remains alive during the parallel execution.</p><pre class="m-code"><span class="kt">int</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
<span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">};</span>

<span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">task</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">vec</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">sum</span><span class="p">,</span><span class="w"> </span>
<span class="w">  </span><span class="p">[]</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">r</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// binary reducer operator</span>
<span class="p">);</span>
<span class="n">executor</span><span class="p">.</span><span class="n">run</span><span class="p">(</span><span class="n">taskflow</span><span class="p">).</span><span class="n">wait</span><span class="p">();</span>

<span class="n">assert</span><span class="p">(</span><span class="n">sum</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">100</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">55</span><span class="p">);</span></pre><p>The order in which the binary operator is applied to pairs of elements is <em>unspecified</em>. In other words, the elements of the range may be grouped and rearranged in arbitrary order. The result and the argument types of the binary operator must be consistent with the input data type.</p></section><section id="ParallelReductionCaptureIteratorsByReference"><h2><a href="#ParallelReductionCaptureIteratorsByReference">Capture Iterators by Reference</a></h2><p>You can pass iterators by reference using <a href="https://en.cppreference.com/w/cpp/utility/functional/ref">std::<wbr />ref</a> to marshal parameter update between dependent tasks. This is especially useful when the range is unknown at the time of creating a parallel-reduction task, but needs initialization from another task.</p><pre class="m-code"><span class="kt">int</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
<span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
<span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;::</span><span class="n">iterator</span><span class="w"> </span><span class="n">first</span><span class="p">,</span><span class="w"> </span><span class="n">last</span><span class="p">;</span>

<span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">init</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">emplace</span><span class="p">([</span><span class="o">&amp;</span><span class="p">](){</span>
<span class="w">  </span><span class="n">vec</span><span class="w">   </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">};</span>
<span class="w">  </span><span class="n">first</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">begin</span><span class="p">();</span>
<span class="w">  </span><span class="n">last</span><span class="w">  </span><span class="o">=</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">end</span><span class="p">();</span>
<span class="p">});</span>

<span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">task</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">ref</span><span class="p">(</span><span class="n">first</span><span class="p">),</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">ref</span><span class="p">(</span><span class="n">last</span><span class="p">),</span><span class="w"> </span><span class="n">sum</span><span class="p">,</span><span class="w"> </span>
<span class="w">  </span><span class="p">[]</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">r</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// binary reducer operator</span>
<span class="p">);</span>

<span class="c1">// wrong! must use std::ref, or first and last are captured by copy</span>
<span class="c1">// tf::Task task = taskflow.reduce(first, last, sum, [] (int l, int r) { </span>
<span class="c1">//   return l + r;    // binary reducer operator</span>
<span class="c1">// });</span>

<span class="n">init</span><span class="p">.</span><span class="n">precede</span><span class="p">(</span><span class="n">task</span><span class="p">);</span>

<span class="n">executor</span><span class="p">.</span><span class="n">run</span><span class="p">(</span><span class="n">taskflow</span><span class="p">).</span><span class="n">wait</span><span class="p">();</span>

<span class="n">assert</span><span class="p">(</span><span class="n">sum</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">100</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">55</span><span class="p">);</span></pre><p>In the above example, when <code>init</code> finishes, <code>vec</code> has been initialized to 10 elements with <code>first</code> and <code>last</code> pointing to the data range of <code>vec</code>. The reduction task will then work on this initialized range as a result of passing iterators by reference.</p></section><section id="A2ParallelTransformationReduction"><h2><a href="#A2ParallelTransformationReduction">Create a Parallel-Transform-Reduction Task</a></h2><p>It is common to transform each element into a new data type and then perform reduction on the transformed elements. Taskflow provides a method, tf::Taskflow::transform_reduce(B first, E last, T&amp; result, BOP bop, UOP uop, P&amp;&amp; part), that applies <code>uop</code> to transform each element in the specified range and then perform parallel reduction over <code>result</code> and transformed elements. It represents the parallel execution of the following reduction loop:</p><pre class="m-code"><span class="k">for</span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">itr</span><span class="o">=</span><span class="n">first</span><span class="p">;</span><span class="w"> </span><span class="n">itr</span><span class="o">&lt;</span><span class="n">last</span><span class="p">;</span><span class="w"> </span><span class="n">itr</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w">  </span><span class="n">result</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bop</span><span class="p">(</span><span class="n">result</span><span class="p">,</span><span class="w"> </span><span class="n">uop</span><span class="p">(</span><span class="o">*</span><span class="n">itr</span><span class="p">));</span>
<span class="p">}</span></pre><p>The example below transforms each digit in a string to an integer number and then sums up all integers in parallel.</p><pre class="m-code"><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;12345678&quot;</span><span class="p">;</span>
<span class="kt">int</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span>
<span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">task</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">transform_reduce</span><span class="p">(</span><span class="n">str</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">sum</span><span class="p">,</span>
<span class="w">  </span><span class="p">[]</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">      </span><span class="c1">// binary reduction operator</span>
<span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
<span class="w">  </span><span class="p">},</span><span class="w">  </span>
<span class="w">  </span><span class="p">[]</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span><span class="w">     </span><span class="c1">// unary transformation operator</span>
<span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="sc">&#39;0&#39;</span><span class="p">;</span>
<span class="w">  </span><span class="p">}</span><span class="w">   </span>
<span class="p">);</span><span class="w"> </span>
<span class="n">executor</span><span class="p">.</span><span class="n">run</span><span class="p">(</span><span class="n">taskflow</span><span class="p">).</span><span class="n">wait</span><span class="p">();</span><span class="w"> </span>
<span class="n">assert</span><span class="p">(</span><span class="n">sum</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">6</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">8</span><span class="p">);</span><span class="w">  </span><span class="c1">// sum will be 36 </span></pre><p>The order in which we apply the binary operator on the transformed elements is <em>unspecified</em>. It is possible that the binary operator will take <em>r-value</em> in both arguments, for example, <code>bop(uop(*itr1), uop(*itr2))</code>, due to the transformed temporaries. When data passing is expensive, you may define the result type <code>T</code> to be move-constructible.</p></section><section id="ParallelReductionCfigureAPartitioner"><h2><a href="#ParallelReductionCfigureAPartitioner">Configure a Partitioner</a></h2><p>You can configure a partitioner for parallel-reduction tasks to run with different scheduling methods, such as guided partitioning, dynamic partitioning, and static partitioning. The following example creates two parallel-reduction tasks using two different partitioners, one with the static partitioning algorithm and another one with the guided partitioning algorithm:</p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">StaticPartitioner</span><span class="w"> </span><span class="n">static_partitioner</span><span class="p">;</span>
<span class="n">tf</span><span class="o">::</span><span class="n">GuidedPartitioner</span><span class="w"> </span><span class="n">guided_partitioner</span><span class="p">;</span>

<span class="kt">int</span><span class="w"> </span><span class="n">sum1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100</span><span class="p">,</span><span class="w"> </span><span class="n">sum2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
<span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">};</span>

<span class="c1">// create a parallel-reduction task with static partitioner</span>
<span class="n">taskflow</span><span class="p">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">vec</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">sum1</span><span class="p">,</span><span class="w"> </span>
<span class="w">  </span><span class="p">[]</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">r</span><span class="p">;</span><span class="w"> </span><span class="p">},</span>
<span class="w">  </span><span class="n">static_partitioner</span>
<span class="p">);</span>

<span class="c1">// create a parallel-reduction task with guided partitioner</span>
<span class="n">taskflow</span><span class="p">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">vec</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">sum2</span><span class="p">,</span><span class="w"> </span>
<span class="w">  </span><span class="p">[]</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">r</span><span class="p">;</span><span class="w"> </span><span class="p">},</span>
<span class="w">  </span><span class="n">guided_partitioner</span>
<span class="p">);</span></pre><aside class="m-note m-info"><h4>Note</h4><p>By default, parallel-reduction tasks use <a href="namespacetf.html#a66b72776c788898aee9e132b0ea9b405" class="m-doc">tf::<wbr />DefaultPartitioner</a> if no partitioner is specified.</p></aside></section>
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